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Braiding of the attractor and the failure of iterative algorithms

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References

  • [BR] Bers, L., Royden, H.: Holomorphic families of injections. Acta Math. 157, 259–286 (1986)

    Google Scholar 

  • [Bi] Birman, J.: Braids, Links and Mapping Class Groups. Ann Math. Stud.82, Princeton, 1974

  • [BI] Blanchard, P.: Complex analytic dynamics on the Riemann sphere. Bull. AMS11, 85–141 (1984)

    Google Scholar 

  • [DM] Doyle, P., McMullen, C.: Solving the quintic by iteration (In preparation)

  • [FLP] Fathi, A., Laudenbach, F., Poenaru, V.: Travaux de Thurston sur les Surfaces. Asterisque, Vol. 66–67 (1979)

  • [FS] Flexor, M., Sentenac, P.: Preprint, Orsay

  • [G] Gilman, J.: Structure of elliptic irreducible subgroups of the modular group. Proc. Lond. Math. Soc.47, 27–42 (1983)

    Google Scholar 

  • [Ker] Kerckhoff, S.: The Nielsen realization problem. Ann. Math.117, 235–265 (1983)

    Google Scholar 

  • [MSS] Mane, R., Sad, P., Sullivan, D.: On the dynamics of rational maps. Ann. Sci. Ec. Norm. Super.16, 193–217 (1983)

    Google Scholar 

  • [Mc1] McMullen, C.: Families of rational maps and iterative root-finding algorithms. Ann. Math.125, 467–493 (1987)

    Google Scholar 

  • [Mc2] McMullen, C.: Automorphisms of rational maps. (To appear, MSRI Geometric Function Theory Proceedings)

  • [SS] Shub, M., Smale, S.: On the existence of generally convergent algorithms. J. Complex.2, 2–11 (1986)

    Google Scholar 

  • [Sm] Smale, S.: On the efficiency of algorithms of analysis. Bull. AMS13, 87–121 (1985)

    Google Scholar 

  • [Sul1] Sullivan, D.: Conformal dynamical systems. In: Geometric Dynamics. (Lect. Notes Math., vol. 1007, pp. 725–752) Berlin Heidelberg New York: Springer 1983

    Google Scholar 

  • [Sul2] Sullivan, D.: Quasiconformal homeomorphisms and dynamics III: Topological conjugacy classes of analytic endomorphisms (Preprint)

  • [ST] Sullivan, D., Thurston, W.: Extending holomorphic motions. Acta Math.157, 243–258 (1986)

    Google Scholar 

  • [W] Whyburn, G.: Analytic Topology. AMS Coll. Publ.28, 1942

  • [Z] Zieschang, H.: Finite Groups of Mapping Classes of Surfaces. Lect. Notes Math. vol. 875. Berlin Heidelberg New York: Springer 1981

    Google Scholar 

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Research partially supported by NSF Grant 8120790

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McMullen, C. Braiding of the attractor and the failure of iterative algorithms. Invent Math 91, 259–272 (1988). https://doi.org/10.1007/BF01389368

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